On a family of singular continuous measures related to the doubling map
Dynamical Systems
2022-10-19 v2
Abstract
Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue--Morse measure.
Keywords
Cite
@article{arxiv.2006.09755,
title = {On a family of singular continuous measures related to the doubling map},
author = {Michael Baake and Michael Coons and James Evans and Philipp Gohlke},
journal= {arXiv preprint arXiv:2006.09755},
year = {2022}
}
Comments
15 pages, with illustrating examples and figures, revised and slightly expanded version